2021/08/19 by Lê Tuâń Hoa, Le Tuan Hoa, Hoa, Le Tuan
Computer Science · Mathematics · #13F20 #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #msc:13F20
paper · pdf · doi:10.48550/arxiv.2108.08564
Submitted to Acta Math. Vietnam
arxiv created 2021/08/19 · openalex publication_date 2021/08/19 · arxiv updated 2021/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The degree excess function ε(I;n) is the difference between the maximal generating degree d(In) of a homogeneous ideal I of a polynomial ring and p(I)n, where p(I) is the leading coefficient of the asymptotically linear function d(In). It is shown that any non-increasing numerical function can be realized as a degree excess function, and there is a monomial ideal I whose ε(I;n) has exactly a given number of local maxima. In the case of monomial ideals, an upper bound on ε(I;n) is provided. As an application it is shown that in the worst case, the so-called stability index of the Castelnuovo-Mumford regularity of a monomial ideal I must be at least an exponential function of the number of variables.